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" Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units. "
Elements of Geometry - Page 101
by Adrien Marie Legendre - 1825 - 224 pages
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A Treatise on Algebra

Elias Loomis - Algebra - 1855 - 356 pages
...large, because the divisor is too small. We therefore complete the divisor by adding to it three times the product of the tens by the units, plus the square of the units. The entire operation is then as follows : 12-167]23=the root. 8 20'X3 =1200 20 X3X3 = 180 3'= 9 4167...
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The Elements of Algebra

Elias Loomis - Algebra - 1856 - 280 pages
...see that the square of a number composed of tens and units contains the square of the tens plus twice the product of the tens by the units, plus the square of the units. Now the square of tens can give no significant figure in the first right-hand period ; the square of...
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A Treatise on Algebra

Elias Loomis - Algebra - 1858 - 394 pages
...large, because the divisor is too small. We therefore complete the divisor by adding to it three times the product of the tens by the units, plus the square of the units. The entire operation is then as follows : 12-167|23=the root 8 20'X3 =1200 20 X3X3= 180 3'= 9 4167...
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New Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1860 - 332 pages
...- &• + (2x + y)y. That is, the number is equal to the square of the tens in its roots, plus twice the. product of the tens by the units, plus the square of the units. EXAMPLE. 1. Extract the square root of 6084. Since this number is composed of more than two places...
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A Course of Mathematics: Composed for the Use of the Royal Military Academy

Charles Hutton - Mathematics - 1860 - 1014 pages
...second period 41, and annexing them on the right of 4, the result is 441, a number which contains tnice the product of the tens by the units, plus the square of the units. We may further prove, as in the last case, that if we point off the last figure 1, and divide the preceding...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1860 - 412 pages
...the two next figures 84. The result of this operation is 1184, and this ntimber is made up of twice the product of the tens by the units plus the square of the units. But since tens multiplied by units cannot give a product of a lower order than tens, it follows that...
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Elementary Algebra: Embracing the First Principles of the Science

Charles Davies - Algebra - 1861 - 322 pages
...proves that the square of a number composed of tens and units, equals the square of the lens plus twice the product of the tens by the units, plus the square of the units. 94. If now, we make the units 1, 2, 3, 4, &c., tens, or units of the second order, by annexing to each...
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The R.I. Schoolmaster, Volume 7

Education - 1861 - 526 pages
...period must be the square of the tens. After taking out this square of the tens, we have left the double product of the tens by the units plus the square of the units. By dividing the double product by double the tens, we find the units. BY inspection, we may often determine...
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New Elementary Algebra: in which the First Principles of Analysis are ...

Benjamin Greenleaf - 1863 - 338 pages
...that is the square of 60, from the given number, we have the remainder 756, which must contain twice the product of the tens by the units, plus the square of the units, or 2 ab -|- b3. Dividing this remainder by 2 a, that is by 120, gives 6, which is the value of 6. Then...
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A Treatise on Algebra

Elias Loomis - Algebra - 1864 - 386 pages
...large, because the divisor is too small. We therefore complete the divisor by adding to it three times the product of the tens by the units, plus the square of the units. The entire operation is then as follows: 12-167|23=the root. 8 20'X 3 =1200 4167 20 X3X3 = 180 3'=...
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